If they have no evidence that this was because you didn't tighten the bolts properly then they don't have reasonable grounds to dismiss you. I presume you have worked there for more than 2 years as otherwise you cant make a claim. Assuming you have, however, you should see your solicitor about submitting a claim. The employer has to do a full investigation and reach a "reasonable belief" that you acted in a way as to justify summary dismissal. I don't see how they can do that where the customer had the car out for some time and had covered a high mileage. Happy to discuss further. I hope that helps. Please leave a positive rating so that I am credited for my time.
There not necessarily a contractual right to a reference there is not usually a contractual right to a reference at all. I would concentrate on a claim for unfair dismissal and if there is an offer to settle that you can ask for a reference as part of the negotiation.